### Problem Statement

Given a positive integer N with at least two digits, we can define magic(N) as follows: Write N as a string of decimal digits. Now, for each two consecutive digits, compute their difference (a non-negative number less than ten), and write it down. In this way you'll obtain a new number, possibly with leading zeroes. Drop unnecessary leading zeroes if there are any.

For example, magic(5913)=482, magic(1198)=081=81, and magic(666)=00=0.

For any number N the sequence: N, magic(N), magic(magic(N)), ... will sooner or later terminate with a single-digit number. This final value is called the magic fingerprint of N.

For example, for N=5913 we get the sequence: 5913, 482, 46, 2. Therefore the magic fingerprint of 5913 is 2.

There are not too many numbers with the magic fingerprint seven (7). These numbers are considered lucky.

Write a method that will compute the count of lucky numbers between A and B, inclusive.

### Definition

 Class: MagicFingerprint Method: countLuckyNumbers Parameters: int, int Returns: int Method signature: int countLuckyNumbers(int A, int B) (be sure your method is public)

### Constraints

-B will be between 1 and 1,000,000,000, inclusive.
-A will be between 1 and B, inclusive.

### Examples

0)

 `1` `9`
`Returns: 1`
 The only single-digit lucky number is, of course, the lucky number seven.
1)

 `1` `100`
`Returns: 6`
 There are five two-digit lucky numbers: 18, 29, 70, 81, and 92.
2)

 `1198` `1198`
`Returns: 1`
 The number 1198 is lucky. The corresponding sequence is: 1198, 81, 7.
3)

 `1223` `1299`
`Returns: 0`
 This range contains no lucky numbers.
4)

 `999999930` `1000000000`
`Returns: 2`
 The two lucky numbers in this range are 999,999,980 and 999,999,992.
5)

 `100000` `1000000000`
`Returns: 159720`
 The largest output is obviously not much larger.

#### Problem url:

http://www.topcoder.com/stat?c=problem_statement&pm=8600

#### Problem stats url:

http://www.topcoder.com/tc?module=ProblemDetail&rd=12007&pm=8600

misof

#### Testers:

PabloGilberto , legakis , Olexiy , ivan_metelsky

#### Problem categories:

Brute Force, Recursion, Search